Power law scaling of test error versus number of training images for deep convolutional neural networks

The highest accuracy in image classification is of utmost importance for the industrial application of algorithms based on convolutional neural networks. Empirically, it is sometimes possible to improve accuracy by increasing the size of the training set. In this work, the scaling of the test accuracy versus the size of the training set was studied for different networks. First, a network with a depth of few layers was initialized with random parameters and trained on subsets of images of variable size sampled from the MNIST dataset of handwritten digits and MNIST fashion dataset of clothes and accessories. The scaling of the accuracy versus the size of the training set may be described as the sum of two components: a power law and an offset independent on the size of the training set. Exponent of the power law appears to be the same in both dataset and independent on seeds, initial weights and number of convolutional filters. Then, the scaling of the accuracy versus the size of training set has been evaluated on a dataset of pictures of paintings, sacred icons and sculptures with the goal to correctly classify unknown pictures. The networks chosen are the ones implemented in the machine vision library Halcon 18.11, including two convolutional neural networks with unknown topology and Resnet50, pretrained on industrial images. The scaling of the accuracy versus the size of the training set seems to be compatible with the power law scaling observed on the few layers network trained on MNIST.